whence
For use in accurate observations, corrections are required for temperature, humidity and variation in the force of gravity.
La Place’s formula which includes terms derived from the consideration of these conditions is obtained as follows:
Suppose a portion of the atmosphere included between two stations at different altitudes to be divided into very thin laminæ.
Let z be the distance of one of these from the surface of the globe and dz its thickness.
Let P be the pressure upon a unit of surface upon the lower side of this layer; and W the weight per cubic meter of the air at this pressure.
Then the pressure on the upper side will be less than P by an amount equal to the weight of a column of air whose base is a unit and height is equal to dz.
Whence